In this paper, we introduce a new composite spectral indices αγxγ = αxγ - αγ, and prove [Formula: see text], that means αγxγ is intrinsic. We plot a αxox - αγxγ diagram for 25 Gev γ-ray blazars for which αx and αγ have been provided in the literature, where αxox = αox - αx which was introduced by Sambruna et al. (1996) and proved that it is intrinsic by our previous paper (Xie et al. 2001). Using this new composite color–color (αxox - αγxγ) diagram, we investigated the nature of the HBLs–LBLs relationship, and the BL Lacs–FSRQs relationship, in high-energy emission. The results show that the spectral energy distributions of three subclasses of Gev γ-ray loud blazars are different, but essentially continuous: HBLs and FSRQs occupy separated regions while LBLs bridge the gap between HBLs and FSRQs. The results are consistent with that derived from a low energy color–color(αxox - αoro) diagram by Sambruna et al. (1996) and Xie et al. (2001). However, on the αox - αxγ diagram, FSRQs, LBLs and HBLs occupy same region. Because both αγxγ and αxox are intrinsic, thus, the new connection among HBLs, LBLs and FSRQs obtained by us is intrinsic.

In this paper, we investigated the issue of black hole masses and minimum timescales of jet emission for blazars. We proposed a sophisticated model that sets an upper limit to the central black hole masses M • with the minimum timescales Δt min ob of variations observed in blazars. The value of Δt min ob presents an upper limit to the size of the blob in the jet. The blob is assumed to be generated in the jet-production region in the vicinity of the black hole, and then the expanding blob travels outward along the jet. We applied the model to 32 blazars, 29 of which were detected in gamma-rays by satellites, and these Δt min ob are on the order of hours, with large variability amplitudes. In general, the M • estimated with this method are not inconsistent with those masses reported in the literature. This model is natural for connecting M • with Δt min ob for blazars, and seems to be applicable in constraining M • in the central engines of blazars.

Based on the gravitational redshift, one prediction of Einstein's general relativity theory, of broad optical emission lines in active galactic nuclei (AGNs), a new method is proposed to estimate the virial factors f in measuring black hole masses M RM by the reverberation mapping of AGNs. The factors f can be measured on the basis of two physical quantities, i.e. the gravitational redshifts z g and full widths at half maxima v FWHM of broad lines. In the past it has been difficult to determine the factors f for individual AGNs. We apply this new method to several reverberation mapped Seyfert 1 galaxies. There is a correlation between f and broad-line region (BLR) radius r BLR , f = 5.4r 0.3 BLR , for the gravitationally redshifted broad lines He II, He I, Hβ and Hα in narrow-line Seyfert 1 galaxy (NLS1) Mrk 110. This correlation results from the radiation pressure influence of the accretion disc on the BLR clouds. The radiation pressure influence seems to be more important than usually thought in AGNs. Mrk 110 has f ≈ 8-16, distinctly larger than the mean f ≈ 1, usually used to estimate M RM in the case of v FWHM . NGC 4593 and NLS1 Mrk 486 has f ≈ 3 and f ≈ 9, respectively. Higher f values of several tens are derived for three other NLS1s. There is a correlation between f and accretion rateṀ f =1 , f = 6.8Ṁ−2 as f = 1 is assumed to estimate M RM used in the Eddington luminosity L Edd ,Ṁ • is the mass accretion rate, and c is the speed of light. These larger f values will produce higher M RM values and lower Eddington ratios.